Listen to Robert Emmerich introduce The Big Apple, a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.

Wikipedia: Hot cross bun
A hot cross bun is a spiced sweet bun made with currants or raisins, marked with a cross on the top, and traditionally eaten on Good Friday in Australia, British Isles, Canada, India, New Zealand, Pakistan, South Africa and some parts of America. The buns mark the end of Lent and different parts of the hot cross bun have a certain meaning, including the cross representing the crucifixion of Jesus, and the spices inside signifying the spices used to embalm him at his burial. They are now available all year round in some places. Hot cross buns may go on sale in Australia and New Zealand as early as New Year’s Day or after Christmas.

15 September 1978, Nevada State Journal and Reno Evening Gazette (Reno, NV), “Hangin’ Out” by Guy Richardson, Entertainment sec., pg. 3, col. 3:
“What do you get from pouring hot water down a rabbit hole? Hot cross bunnies.”—David Harris, (who is probably over the border by now, so pursuit is pointless).

About a month later I saw the same joke in Reader’s Digest. The just recently the joke was reprised several times on “The Muppets Go to the Movies.” And now you hear it everywhere.

Google BooksLinguistic Concepts:
An Introduction to Tagmemics
By Kenneth L Pike
Lincoln, NE: University of Nebraska Press
1982
Pg. 129:
Query: If you pour hot water down a rabbit hole, what do you get?
Answer: Hot cross bunnies.

1 March 1982, The Sun (Baltimore, MD, “Cats on canvas: Calif. artist paints them selfish, smug and strange” by Muriel Dobbin, pg. B3, col. 3:
And a rabbit with its ears upright is Mrs. Dizick’s illustration of an old joke about what happens when you pour boiling water down a rabbit hole.

12 April 2003, Daily Press (Timmons, ON), “Easter Internet style: The good, the bad and the corny” by Steve Elliott, pg. 21:
Q. What do you get when you pour hot water down a rabbit hole? A. A hot cross bunny.

Twitter
Ian Sealy‏
@iansealy
Replying to @jemimakiss
@jemimakiss Last attempt before sleep: Q: What do you get when you pour a kettleful of water down a rabbit hole? A: Hot, cross bunnies.
5:49 PM - 21 May 2008

Twitter
James Zhuo‏
@jamesz
What do you get when you pour a kettleful of water down a rabbit hole? A: Hot, cross bunnies. from @iansealy
3:32 AM - 22 May 2008

Google BooksA Prairie Home Companion
Pretty Good Joke Book (6th Edition)
Introduced by Garrison Keillor
Prince Frederick, MD: HighBridge, a division of Recorded Books
2015
Pg. ?:
What do you get when you pour boiling water down a rabbit hole?
Hot cross bunnies.